Metamaterial Inspired Electromagnetic Applications

Transcription

1 Metamaterial Inspired Electromagnetic Applications

2 Balamati Choudhury Editor Metamaterial Inspired Electromagnetic Applications Role of Intelligent Systems CSIR-NAL 123

3 Editor Balamati Choudhury Centre for Electromagnetics CSIR-National Aerospace Laboratories Bangalore, Karnataka India ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer Nature Singapore Pte Ltd This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore , Singapore

4 It takes a minute to find a special person, an hour to appreciate them, and a day to respect them, but it takes an entire lifetime to forget them. This book is dedicated to the entirely unforgettable Dr. R M Jha!

5 Preface The metamaterial science and technology are emerging as a next higher level performance contributor, specifically in the electromagnetic community. After experimental verification of negative refractive index metamaterial in 2001, the research community is focusing on application side and an exponential growth has been observed in various metamaterial electromagnetic applications such as antennas, microwave devices, high NA lenses, and radar absorbers. Electromagnetic (EM) designs including metamaterial being complex and nonlinear in nature optimization play an important role. In this book, we focus on role of soft computing technique-based EM computational engines in design and optimization of a wide range of electromagnetic applications. Apart from the theoretical background of metamaterials and soft computing techniques, this contributed volume includes novel electromagnetic applications such as tensor analysis for invisibility cloaking, metamaterial structures for cloaking applications, broadband radar absorbers and antennas. Chapter 1 gives an insight to background theory of metamaterial and soft computing techniques. The fundamental principle of metamaterial and their properties have been discussed. Toward optimization of these structures, various soft computing algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), and bacterial foraging optimization (BFO) have been described. Various types of metamaterial unit cells and their design and optimization procedures using soft computing techniques have been detailed along with the development of soft computing-based electromagnetic computational engine. Planar inverted F antennas (PIFA) have wide range of applications in wireless industry. These antennas are also used as wireless sensors in aircraft fuel tanks to check the fuel availability status. Chapter 2 explores the advancements in design optimization of PIFA systems. The literature reveals that the antenna size can significantly be reduced by introducing metamaterial structures. Hence, design optimization of a metamaterial-loaded compact planar inverted F antenna has been carried out and reported systematically. The optimized antenna shows a return loss of db, whereas the conventional PIFA is of db only. vii

6 viii Preface Chapter 3 provides an insight into the scalars, vectors, and tensors in electromagnetics and the significance of their analysis in the aerospace domain. The fundamental mathematical concepts of scalars, vectors, and tensors are being explained, and a thorough investigation on the relevance of these parameters in electromagnetics, cloaking, and various other aerospace applications has been conducted. This chapter connects to the detail design of metamaterial cloaking and optimization of conformal unit cells in the subsequent chapters. In recent years, the radar cross section (RCS) reduction characteristics of cloaking structures have been widely investigated as it found extensive applications in stealth platform. Chapter 4 deals with the design of ideal circular, cylindrical, and spherical cloaking structures in accordance with transformation optics theory. The simulations are performed by using finite element method (FEM)-based COMSOL Multiphysics software. The performance of the designed ideal spherical cloak is analyzed by comparing the RCS of PEC sphere without cloaking shells and with multilayer cloaking shells. It has been observed that multilayer spherical cloak shows reduced RCS in C band with respect to the PEC sphere. Further, the analysis of particle ray trajectories has been carried out by performing geometric ray tracing. Conformal metamaterial multilayer analysis for design and simulation of invisibility cloak is a challenging task because of the curvature effects of the platform. Chapter 5 gives the analysis of material properties of various conformal metamaterial unit cell structures patterned on the cloaking layers. Design and simulation of planar and nonplanar metamaterial unit cells have been carried out and reported systematically. The extracted permittivity and permeability characteristics of the conformal metamaterial structures are compared with corresponding planar one. Further analysis of effect of radius of curvature of the platform has been studied and explained briefly. The advances in artificial engineered materials such as metamaterials have created a wide interest in military aviation scientific community. The researches in modern military aviation are endowed with techniques based on low observable platforms. Design and development of metamaterial-based radar absorbers are one of the cutting edge technologies in this domain. Design and development of two metamaterial-based broadband microwave absorbers have been carried out and described in Chap. 6. Further, the proposed structures have been optimized for absorption in the entire X band, using soft computing-based computational engine. The proposed pentagon-shaped metamaterial structure and novel metamaterial structures have been fabricated, and backscattered signal power from the test samples is measured and compared with backscattered signal power from PEC of same footprint. The measurement result ensures the broadband absorption capability of proposed structures in the X band. Bangalore, India Balamati Choudhury

7 Acknowledgements At the outset, I wish to thank Mr. Jatinder J Jadhav, Director, and Dr. Jatinder Singh, Cluster Chairman, Systems Engineering Cluster of CSIR-National Aerospace Laboratories, Bangalore for sustained support and official permission to write this contributed volume. I would also like to acknowledge valuable suggestions from Dr. R.U. Nair, Head, Centre for Electromagnetics, CSIR-National Aerospace Laboratories and his invaluable support during the course of writing this book. Beyond the technical aspects, correction of grammatical error is also a very pertinent area. I would like to extend my thanks to Ms Anusha Eldo for her help in going through the entire book for syntax error editing. It is our pleasure to acknowledge all the authors of this contributed volume who have completed their research work as project scientists at CSIR-National Aerospace Laboratories. Indeed their work carried out at Centre for Electromagnetics, CSIR-National Aerospace Laboratories has been adapted here as book chapters of this book. We thank them for transferring the necessary copyrights for facilitating the production and circulation of the book in hand. The publisher s effort plays a very important role in writing a book on scheduled time. Swati Meherishi, Executive Editor at Springer has always been very responsive in this regard and I would like to thank her for all her inputs. Needless to mention the gratefulness, Balamati owes to her uncle Mr. Bipin Padhy for his blessings and constant encouragement during the course of writing this book. Balamati Choudhury ix

8 Contents 1 Soft Computing for Metamaterial Structures... 1 Balamati Choudhury 2 Metamaterial-Based Miniaturized Planar Inverted-F Antenna S. Manjula and Balamati Choudhury 3 Electromagnetic Perspective of Tensors Susan Thomas and Balamati Choudhury 4 Design and Optimization of Multilayer Ideal Cloak M.H. Jyothi and Balamati Choudhury 5 Design Optimization of Cloaks Pavani V. Reddy, Susan Thomas and Balamati Choudhury 6 Design Optimization of Broadband Radar Absorbing Structures Anusha Eldo and Balamati Choudhury xi

9 About the Editor Dr. Balamati Choudhury is a scientist at the Centre for Electromagnetics of the CSIR-National Aerospace Laboratories, Bangalore, India. She received her M. Tech. (ECE) degree from the National Institute of Science and Technology (NIST), India, and Ph.D. (Eng.) degree in microwave engineering from Biju Patnaik University of Technology (BPUT), India, in From 2006 to 2008, she was a senior lecturer at the Department of Electronics and Communication at the NIST, Orissa, India. Her research and teaching interests are in the domain of soft computing techniques in electromagnetic design and optimization, computational electromagnetics for aerospace applications, metamaterial design applications, radio frequency (RF), and microwaves. She has contributed to a number of projects, including the development of ray tracing techniques for RF analysis of propagation in an indoor environment, low radar cross section (RCS) design, phased arrays and adaptive arrays, and conformal antennas. She was also the recipient of the CSIR-NAL Young Scientist Award for the year for her contribution in the area of computational electromagnetics for aerospace applications. Dr. Balamati has authored or co-authored over 140 scientific research papers and technical reports, five SpringerBriefs, and three book chapters as well as a book entitled: Soft Computing in Electromagnetics: Methods and Applications. Dr. Balamati is also an assistant professor of the Academy of Scientific and Innovative Research (AcSIR), New Delhi. xiii

10 Abbreviations DNM EBG FEM FSS GSM LHM PBG PIFA PSO SAR SRR VBA Double negative materials Electromagnetic band gap Finite element methods Frequency-selective surface Global system for mobile communication Left-handed materials Photonic band gap Planar inverted F antenna Particle swarm optimization Specific absorption rate Spilt ring resonator Visual basic for applications xv

11 List of Figures Figure 1.1 Figure 1.2 Figure 1.3 a Right-handed orientation of vectors E, H, K when e r >0,µ r >0.bLeft-handed orientation of vectors E, H, K when e r <0,µ r < Reflection and refraction at the interface of two media when a n 2 > 0 (ray 3), b n 2 < 0 (ray 4)... 2 Common metamaterial designs, a circular split-ring resonator, b electric ring resonator, c multi-band circular ring metamaterial structure, d square ring resonator... 3 Figure 1.4 Flowchart of optimization techniques... 5 Figure 1.5 Basic structure neural network Figure 1.6 Swarm behavior during the search of food... 7 Figure 1.7 Flow of genetic algorithm Figure 1.8 Single point crossover Figure 1.9 Two-point crossover Figure 1.10 Uniform crossover Figure 1.11 Mutation operation in genetic algorithm Figure 1.12 Flowchart of PSO algorithm Figure 1.13 Structure of double square split-ring resonator Figure 1.14 Equivalent circuit of square split-ring resonator Figure 1.15 PSO optimized double-ring square SRR designed using FEM solver Figure 1.16 Extracted characteristics of the modeled double-ring square SRR, a permittivity, b permeability Figure 1.17 a Schematic of circular SRR along with dimensions. b Distributed circuit represented by corresponding lumped network Figure 1.18 Unit cell of the CSRR designed Figure 1.19 Reflection and transmission characteristics of the designed CSRR structure xvii

12 xviii List of Figures Figure 1.20 Extracted permittivity and permeability of the designed CSRR Figure 1.21 Negative permeability at the desired resonant frequency Figure 1.22 Schematic of computational engine based on optimization algorithm Figure 2.1 Schematic of a conventional PIFA system Figure 2.2 Capacitive-loaded antenna Figure 2.3 A simple square split ring resonator Figure 2.4 Structure of PIFA without metamaterials Figure 2.5 Structure of proposed PIFA design with metamaterial Figure 2.6 Return loss characteristics of conventional PIFA structure Figure 2.7 Radiation pattern of the conventional PIFA structure Figure 2.8 Impedance plot (phi = 90) of conventional PIFA structure Figure 2.9 Polar plot (phi = 0) of the conventional PIFA structure Figure 2.10 Graphical user interface of PSO-based CAD package for design of metamaterial structures Figure 2.11 Equivalent circuit of square split ring resonator Figure 2.12 Optimized design of square SRR Figure 2.13 Scattering parameters of square SRR Figure 2.14 Extracted permittivity of square SRR Figure 2.15 Extracted permeability of square SRR Figure 2.16 Structure of PIFA design with metamaterials Figure 2.17 Return loss characteristics of PIFA system with metamaterials Figure D radiation pattern (directivity) of PIFA system Figure D radiation pattern (gain) of PIFA system Figure 2.20 Polar plot (phi = 90) of PIFA system Figure 2.21 Polar plot (phi = 0) of PIFA system Figure 2.22 Schematic of a conventional PIFA system Figure 2.23 Return loss (S11) for the conventional PIFA structure Figure 2.24 Radiation pattern of the conventional PIFA structure Figure 2.25 Figure D polar plot (phi = 90) of the conventional PIFA structure D polar plot (phi = 0) of the conventional PIFA structure Figure 2.27 Schematic of a PIFA system with PBG substrate Figure 2.28 Return loss for the PIFA structure with PBG Figure 2.29 Radiation pattern of PIFA structure with PBG Figure 2.30 Radiation pattern (in polar plot (phi = 90)) of the PIFA structure with PBG Figure 2.31 Polar plot (phi = 0) of the PIFA structure with PBG Figure 2.32 Schematic of conventional PIFA Figure 2.33 Return loss characteristics of a conventional PIFA... 58

13 List of Figures xix Figure 2.34 Radiation pattern of the conventional PIFA structure Figure 2.35 Radiation pattern (polar plot (phi = 90)) of the conventional PIFA structure with metamaterials Figure 2.36 Radiation pattern (polar plot (phi = 0)) of the conventional PIFA structure with metamaterials Figure 2.37 Design of metamaterial unit cell Figure 2.38 Scattering parameters of SRR Figure 2.39 Permittivity characteristics of SRR Figure 2.40 Permeability characteristics of SRR Figure 2.41 Schematic of PIFA with metamaterial unit cell Figure 2.42 Return loss characteristics of PIFA with metamaterial unit cell Figure 2.43 Radiation pattern of PIFA with metamaterial unit cell Figure 2.44 Radiation pattern (polar plot (phi = 90)) of PIFA structure with metamaterials Figure 2.45 Radiation pattern (polar plot (phi = 0)) of the PIFA structure with metamaterials Figure 3.1 Tensor components and their directions Figure 3.2 Direction of flux lines for a positive charge, b negative charge, c dipole Figure 3.3 Point charge placed in an electric field Figure 3.4 Direction of force for a like charges and b unlike charges Figure 3.5 Direction of electric field for a positive point charge Figure 3.6 Direction of flux lines (tubes) in a dipole Figure 3.7 Direction of flux lines for a charge +Q Figure 3.8 Point charges placed in an electric field Figure 3.9 Magnetic flux lines in a current-carrying wire Figure 3.10 Magnetic flux density for a straight current-carrying wire Figure 3.11 Magnetic flux density for a current-carrying loop Figure 3.12 Force in a current-carrying wire placed in magnetic field Figure 3.13 Force between two current-carrying wires placed in a magnetic field Figure 3.14 Anisotropic material unpolarized with electric field along x direction Figure 3.15 Anisotropic material strongly polarized with electric field along z direction Figure 3.16 Polarization in a isotropic material and b anisotropic material Figure 4.1 Illusion of cylindrical cloak Figure 4.2 Typical geometry of a circular cylindrical cloak Figure 4.3 2D cylindrical cloak, electric field patterns, with stream lines indicating the direction of power flow

14 xx List of Figures Figure 4.4 2D circular cylindrical cloak with EM wave incident at a 45, b 80, c 200, d Figure 4.5 Typical spherical geometry used for simulation of ideal spherical cloak Figure 4.6 3D visualization of spherical cloak, electric field patterns Figure 4.7 3D visualization of spherical cloak with electromagnetic wave incident at a 60, b Figure 4.8 Computational domain for computing the RCS of a PEC sphere in free space Figure 4.9 Measured RCS plot of the sphere (c.f. Dr. Allen E. [6]) Figure 4.10 Simulated RCS plot of the PEC sphere Figure 4.11 Computational domain for computing the RCS of a one-layer cloaking shell in free space Figure 4.12 RCS plot of the one-layer cloaking shell with respect to a/k (color online) Figure 4.13 Computational domain for computing the RCS of two-layer cloaking shell in free space Figure 4.14 RCS plot of the two-layer cloaking shell with respect to a/k Figure 4.15 Computational domain for computing the RCS of three-layer cloaking shell in free space Figure 4.16 RCS plot of the three-layer cloaking shell with respect to a/k Figure 4.17 Computational domain for computing the RCS of four-layer cloaking shell in free space Figure 4.18 RCS plot of the four-layer cloaking shell with respect to a/k Figure 4.19 RCS comparison plot between PEC and multilayer cloaking shell with respect to a/k (color online text) Figure 5.1 Design of SRR unit cell Figure 5.2 Magnitude of transmission parameters (S 21 ) for SRR unit cell Figure 5.3 Phase of transmission parameters (S 21 ) for SRR unit cell Figure 5.4 Extracted permittivity (real) versus frequency Figure 5.5 Extracted permittivity (imaginary) versus frequency Figure 5.6 Extracted permeability (real) versus frequency Figure 5.7 Extracted permeability (imaginary) versus frequency Figure 5.8 Metamaterial unit cells stacked along the direction of electric field Figure 5.9 Transmission (S 21 ) parameters of metamaterial array Figure 5.10 Metamaterial unit cells stacked along the direction of wave propagation Figure 5.11 Transmission (S 21 ) parameters of metamaterial array

15 List of Figures xxi Figure 5.12 Splitting of resonance in an array of 5 unit cells stacked along the wave propagation vector Figure 5.13 Metamaterial unit cells stacked along the direction of electric field with alternative orientation Figure 5.14 Transmission (S 21 ) parameters of metamaterial array shown in Fig Figure 5.15 Finite two-dimensional metamaterial array (3 3) Figure 5.16 Transmission (S 21 ) parameters of metamaterial array shown in Fig Figure 5.17 Design of a layer of the cylindrical microwave cloaking structure with SRR unit cells Figure 5.18 a Typical proposed planar I-shaped unit cell. b Typical designed conformal I-shaped unit cell Figure 5.19 Scattering parameters (S 11 and S 21 ) of planar unit cell structure of proposed planar I shape Figure 5.20 Scattering parameters (S 11 and S 21 ) of designed conformal I-shaped unit cell structure Figure 5.21 a Permeability characteristics of planar I-shaped unit cell. b Permeability characteristics of conformal I-shaped unit cell Figure 5.22 a Permittivity characteristics of planar I-shaped unit cell. b Permittivity characteristics of conformal I-shaped unit cell Figure 5.23 Refractive index of proposed a planar I-shaped unit cell, b conformal I-shaped unit cell Figure 5.24 a Typical proposed planar H-shaped unit cell. b Typical designed conformal H-shaped unit cell Figure 5.25 Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar H shape Figure 5.26 Scattering parameters (S 11 and S 21 ) of designed conformal H shape Figure 5.27 a Permeability characteristics of proposed planar H shape. b Permeability characteristics of designed conformal H shape Figure 5.28 a Permittivity characteristics of proposed planar H shape. b Permittivity characteristics of designed conformal H shape Figure 5.29 a Typical proposed planar RAM-type unit cell. b Typical designed conformal H shape Figure 5.30 a Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar RAM-type unit cell Figure 5.31 Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal RAM-type unit cell

16 xxii Figure 5.32 Figure 5.33 Figure 5.34 Figure 5.35 Figure 5.36 Figure 5.37 Figure 5.38 Figure 5.39 Figure 5.40 Figure 5.41 Figure 5.42 Figure 5.43 Figure 5.44 Figure 5.45 Figure 5.46 Figure 5.47 Figure 5.48 Figure 5.49 Figure 5.50 Figure 5.51 List of Figures Permittivity characteristics of proposed a planar RAM-type unit cell, b conformal RAM-type unit cell Permeability characteristics of proposed a planar RAM-type unit cell, b conformal RAM-type unit cell a Typical proposed planar square-shaped unit cell, b typical designed conformal square-shaped unit cell Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar square shape Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal square shape a Permeability characteristics of proposed planar square-shaped unit cell, b permeability characteristics of designed conformal square-shaped unit cell Permittivity characteristics of proposed a planar square-shaped unit cell, b conformal square-shaped unit cell Schematic of a planar double-square-shaped unit cell, b designed conformal double-square-shaped unit cell Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar double-square-shaped unit cell Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal double-square-shaped unit cell Permittivity characteristics of a planar double-square-shaped unit cell, b conformal double-square-shaped unit cell Permeability characteristics of a planar double-square-shaped unit cell, bconformal double-square-shaped unit cell a Typical proposed planar middle line SRR unit cell, b conformal middle line SRR unit cell Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar middle line SRR Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal middle line SRR a Permittivity characteristics of proposed middle line SRR, b permittivity characteristics of designed conformal middle line SRR Permeability characteristics of a planar middle line SRR, b conformal middle line SRR a Typical proposed planar OSRR unit cell, b typical designed conformal OSRR unit cell Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar OSRR Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal OSRR

17 List of Figures xxiii Figure 5.52 a Permittivity characteristics of proposed planar OSRR, b permittivity characteristics of designed conformal OSRR Figure 5.53 Permeability characteristics of proposed a planar OSRR, b conformal OSRR Figure 5.54 a Typical proposed planar CSRR unit cell, b typical designed conformal CSRR unit cell Figure 5.55 Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar CSRR Figure 5.56 Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed conformal CSRR Figure 5.57 Permittivity characteristics of proposed a planar CSRR, b conformal CSRR Figure 5.58 Permeability characteristics of a planar CSRR, b designed conformal CSRR Figure 5.59 Schematic of proposed a planar Jerusalem cross unit cell, b conformal Jerusalem cross unit cell Figure 5.60 Scattering parameters (S 11 ) and (S 21 ) characteristics of proposed planar Jerusalem cross unit cell Figure 5.61 Scattering parameters (S 11 ) and (S 21 ) characteristics of designed conformal Jerusalem cross unit cell Figure 5.62 Permittivity characteristics of proposed a planar Jerusalem cross unit cell, b conformal Jerusalem cross unit cell Figure 5.63 Permittivity characteristics of proposed a planar Jerusalem cross unit cell, b conformal Jerusalem cross unit cell Figure 5.64 Array of I-shaped unit cells conformed on a big curvature, b small curvature Figure 5.65 Scattering parameters (S 11 ) and (S 21 ) characteristics of conformal I-shaped unit cell of big curvature Figure 5.66 Scattering parameters (S 11 ) and (S 21 ) characteristics of conformal I-shaped unit cell of small curvature Figure 5.67 Permittivity characteristics of conformal I-shaped unit cells with a big curvature, b small curvature Figure 5.68 Permeability characteristics of conformal I-shaped unit cells with a big curvature, b small curvature Figure 6.1 Schematic of the PSO-based computational engine Figure 6.2 a Schematic of proposed pentagon-shaped metamaterial structure, b reflection characteristics of the proposed structure Figure 6.3 Surface current distribution at resonant frequency GHz in a top layer (pattern), b bottom layer (ground plane)

18 xxiv List of Figures Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Figure 6.11 Figure 6.12 Surface current distribution at resonant frequency GHz in a top layer (pattern) b bottom layer (ground plane) Electric field distribution at resonant frequency of a GHz, b GHz Retrieved material parameters for the designed structure a relative permeability, b relative permittivity c effective impedance Variation in absorption with thickness of dielectric changed from 1.4 to 1.8 mm Variation in absorption with periodicity of structure changed from 8 to 12 mm Variation in absorption with a size of pentagon, b distance to fifth side from center of pentagon Variation in absorption for angle of incidence changed from 0 to 80 in steps of a Unit cell structure for proposed metamaterial absorber. b Absorption characteristics for TE and TM polarizations Surface current distribution at resonant frequency 8.43 GHz in a top layer (pattern), b bottom layer (ground plane) Figure 6.13 Surface current distribution at resonant frequency GHz in a top layer (pattern), b bottom layer (ground plane) Figure 6.14 Electric field distribution at resonant frequencies at a 8.43 GHz, b GHz Figure 6.15 Retrieved material parameters for the designed structure a relative permeability, b relative permittivity, c effective impedance Figure 6.16 Variation in absorption with thickness of dielectric changed from 1.4 to 2.2 mm Figure 6.17 Variation in absorption with periodicity of structure changed from 8 to 11 mm Figure 6.18 Variation in absorption with tail length changed from 1.2 to 2 mm Figure 6.19 Variation in absorption for angle of incidence changed from 0 to 80 in steps of Figure 6.20 Setup for measurement of back-scattered power Figure 6.21 Photograph of the designed pentagon structure test sample Figure 6.22 Back-scattered signals from PEC and pentagon structure in X band Figure 6.23 Back-scattered signals from PEC and pentagon structure in different direction for normal incidence Figure 6.24 Photograph of the designed Novel structure test sample

19 List of Figures Figure 6.25 Figure 6.26 xxv Back-scattered signals from PEC and Novel structure in X band Back-scattered signals from PEC and Novel structure in different direction for normal incidence

20 List of Tables Table 1.1 Comparison of soft computing techniques for optimization of a CSRR at 8.25 GHz (Intel core, 4 GB RAM) Table 2.1 Dimensions of conventional PIFA system Table 2.2 Performance parameters of conventional PIFA system Table 2.3 Dimensions of designed metamaterial Table 2.4 Performance parameters of metamaterial-based PIFA system Table 2.5 Dimensions of PBG-based PIFA system Table 2.6 Performance parameters of conventional PIFA system Table 2.7 Performance parameters of PBG-based PIFA system Table 2.8 Dimensions of conventional PIFA system Table 2.9 Performance parameters of conventional PIFA system Table 2.10 Dimensions of metamaterial unit cell Table 2.11 Performance parameters of PIFA system with metamaterial unit cell Table 5.1 Expression for permittivity and permeability tensors on application of coordinate transformation Table 5.2 Dimensions of SRR unit cell (in millimeters) xxvii